One way to start would be discretize Maxwell's Equations, which can be either represented in an integral form or differential form. For discretizing your spatial domain, I would recommend starting with the differential form of Maxwell's Equations. Start simple and constrain them to one-spatial dimension.
If you can find an analytical solution to the differential equation, that can be easily coded or you can see if MATLAB can solve it for you using the syms function. Otherwise, you can resort to some numerical methods. If you are also looking at time-variant electric fields, I would recommended considering coding a semi-analytical solution via the method of lines (MOLs) (see wikipedia, does a decent job of explaining the concept).
All in all, after that dirty work, you can generate a quiver plot to represent a vector plot for your electric fields using the quiver function in MATLAB. The cool thing about it is that you can implement a for-loop to show how that field involves in time in a single animated figure; which you can save as a video using the writeVideo function in MATLAB.
Does this help?
